essentials of investments with s p bind in card phần 9 ppt

Column B computes income in future years using the growth rate in cell B2; column C computes annual savings by applying the savings rate cell C2 to income; and column E computes consumpt

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AFTER STUDYING THIS CHAPTER YOU SHOULD BE ABLE TO:

Analyze lifetime savings plans

Account for inflation in formulating savings and investmentplans

Account for taxes in formulating savings and investmentplans

Understand tax shelters

Design your own savings plan

This site contains information on asset class returns

and studies on portfolio management.

http://www3.troweprice.com/retincome/RIC

The above site has a simulation retirement planner that

can be used to assess the ability to meet goals under

different allocation strategies.

The sites listed above contain information on personal financial planning.

manage-ment of investmanage-ments In this chapter we are concerned with individual investors’management of their overall lifetime savings plans Our major objective is to

environ-ment in which taxes and inflation interact, rather than to provide a detailed analysis

of the (ever-changing) tax code

Retirement, purchase of a home, and financing the education of children are themajor objectives of saving in most households Inflation and taxes make the task ofgearing investment to accomplish these objectives complex The long-term nature ofsavings intertwines the power of compounding with inflation and tax effects Only themost experienced investors tend to fully integrate these issues into their investmentstrategies Appropriate investment strategy also includes adequate insurance cover-age for contingencies such as death, disability, and property damage

We introduce some of these issues by focusing on one of the long-term goals:formulating a retirement plan We investigate the effect of inflation on the savings

in-corporate Social Security and show how to generalize the savings plan to meet otherobjectives such as owning a home and financing children’s education Finally, we dis-cuss uncertainty about longevity and other contingencies Understanding the spread-sheets we develop along the way will enable you to devise savings/investment plansfor yourself and other households and adapt them to an ever-changing environment

1 Readers in other countries will find it easy to adapt the analysis to the tax code of their own country.

18.1 SAVING FOR THE LONG RUN

In Chapter 17 we described the framework that the Association of Investment Managementand Research (AIMR) has established to help financial advisers communicate with andinvolve client households in structuring their savings/investment plans.2Our objective here

is to quantify the essentials of savings/investment plans and adapt them to environments inwhich investors confront both inflation and taxes As a first step in the process, we set up aspreadsheet for a simple retirement plan, ignoring for the moment saving for other objectives.Before diving in, a brief word on what we mean by saving Economists think of saving as

a way to smooth out the lifetime consumption stream; you save when you have high earnings

in order to support consumption in low-income years In a “global” sense, the concept impliesthat you save for retirement so that consumption during the retirement years will not be toolow relative to consumption during the saving years In a “local” sense, smoothing consump-tion implies that you would finance a large purchase such as a car, rather than buy it for cash.Clearly, local consumption smoothing is of second-order importance, that is, how you pur-chase durable goods has little effect on the overall savings plan, except, perhaps, for very largeexpenditures such as buying a home or sending children to college We begin therefore with asavings plan that ignores even large expenditures and later discuss how to augment the plan toaccount for these needs

A Hypothetical Household

Imagine you are now 30 years old and have already completed your formal education, mulated some work experience, and settled down to plan the rest of your economic life Yourplan is to retire at age 65 with a remaining life expectancy of an additional 25 years Later on,

accu-we will further assume that you have two small children and plan to finance their collegeeducation

For starters, we assume you intend to obtain a (level) annuity for your 25-year retirementperiod; we postpone discussion of planning for the uncertain time of death (You may well live

to over 100 years; what then?) Suppose your gross income this year was $50,000, and youexpect annual income to increase at a rate of 7% per year In this section, we assume that youignore the impact of inflation and taxes You intend to steadily save 15% of income and invest

in safe government bonds that will yield 6% over the entire period Proceeds from your vestments will be automatically reinvested at the same 6% until retirement Upon retirement,your funds in the retirement account will be used to purchase a 25-year annuity (using thesame 6% interest rate) to finance a steady consumption annuity Let’s examine the conse-quences of this framework

in-The Retirement Annuity

We can easily obtain your retirement annuityfrom Spreadsheet 18.1, where we have hiddenthe lines for ages 32–34, 36–44, 46–54, and 56–64 You can obtain all the spreadsheets in thischapter from the Web page for the text: http://www.mhhe.com/bkm

Let’s first see how this spreadsheet was constructed To view the formulas of all cells in

an Excel spreadsheet, choose “Preferences” under the “Tools” menu, and select the box

“Formulas” in the “View” tab The formula view of Spreadsheet 18.1 is also shown on thenext page (numbers are user inputs)

2 If you skipped Chapter 17, you may want to skim through it to get an idea of how financial planners articulate a saver’s objectives, constraints, and investment policy.

Inputs in row 2 include: retirement years (cell A2 ⫽ 25); income growth (cell B2 ⫽ 07);

Age (column A); and income at age 30 (B4 ⫽ 50,000) Column B computes income in future

years using the growth rate in cell B2; column C computes annual savings by applying the

savings rate (cell C2) to income; and column E computes consumption as the difference

be-tween income and savings: column B ⫺ column C Cumulative savings appear in column D

To obtain the value in D6, for example, multiply cell D5 by 1 plus the assumed rate of return

in cell D2 (the ROR) and then add current savings from column C Finally, C40 shows the

sum of dollars saved over the lifetime, and E40 converts cumulative savings (including

inter-est) at age 65 to a 25-year annuity using the financial function PMT from Excel’s function

menu Excel provides a function to solve for annuity levels given the values of the interest

rate, the number of periods, the present value of the savings account, and the future value of

the account: PMT(rate, nper, PV, FV)

We observe that your retirement fund will accumulate approximately $2.5 million (cell

D39) by age 65 This hefty sum shows the power of compounding, since your contributions to

the savings account were only $1.1 million (C40) This fund will yield an annuity of $192,244

per year (E40) for your 25-year retirement, which seems quite attractive, except that the

stan-dard of living you’ll have to get accustomed to in your retirement years is much lower than

your consumption at age 65 (E39) In fact, if you unhide the hidden lines, you’ll see that upon

retirement, you’ll have to make do with what you used to consume at age 51.3This may not

worry you much since, with your children having flown the coop and the mortgage paid up,

you may be able to maintain the luxury to which you recently became accustomed But your

projected well being is deceptive: get ready to account for inflation and taxes

1 If you project an ROR of only 5%, what savings rate would you need to maintain

the same retirement annuity?

Total =SUM(B4:B39) =SUM(C4:C39) Retirement Annuity =PMT($D$2,$A$2,-$D$39,0,0)

3 It would make sense (and would be easy) to rig the retirement fund to provide an annuity with a choice growth rate

to allow your standard of living to grow with that of your social circle We will abstract from this detail here

Concept

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18.2 ACCOUNTING FOR INFL ATION

Inflation puts a damper on your plans in two ways: First, it erodes the purchasing power of the

cumulative dollars you have so far saved Second, the real dollars you earn on your portfolio each year depend on the real interest rate, which, as Chapter 5 showed, is approximately equal

to the nominal rate minus inflation Since an appropriate savings plan must generate a decent

real annuity, we must recast the entire plan in real dollars We will assume your income still is

forecast to grow at a 7% rate, but now you recognize that part of income growth is due to flation, which is running at 3% per year

in-A Real Savings Plan

To convert nominal dollars to real dollars we need to calculate the price level in future yearsrelative to today’s prices The “deflator” (or relative price level) for a given year is that year’sprice level divided by today’s It equals the dollars needed at that future date which provide

the same purchasing power as $1 today (at age 30) For an inflation rate of i⫽ 3%, the tor for age 35 is (1 ⫹ i)5, or in Excel notation, (1 ⫹ i)^5 = 1.03^5 ⫽ 1.16 By age 65, the de-

defla-flator is 2.81 Thus, even with a moderate rate of inflation (3% is below the historical average,

as you can see from Figure 5.4), nominal dollars will lose a lot of purchasing power over long

horizons We also can compute the real rate of return (rROR) from the nominal ROR of 6%:

rROR⫽ (ROR ⫺ i)/(1 + i) ⫽ 3/1.03 ⫽ 2.91%.

Spreadsheet 18.2, with the formula view below it, is the reworked Spreadsheet 18.1adjusted for inflation In addition to the rate of inflation (cell C2) and the real rate of return(F2), the major addition to this sheet is the price level deflator (column C) Instead of nominalconsumption, we present real consumption (column F), calculated by dividing nominalconsumption (column B ⫺ column D) by the price deflator, column C

The numbers have changed considerably Gone is the luxurious retirement we anticipatedearlier At age 65 and beyond, with a real annuity of $49,668, you will have to revert to astandard of living equal to that you attained at age 34; this is less than a third of your realconsumption in your last working year, at age 65 The reason is that the retirement fund of

$2.5 million (E39) is worth only $873,631 in today’s purchasing power (E39/C39) Such is theeffect of inflation If you wish to do better than that, you must save more

Retirement Years Income growth Rate of Inflation Savings rate ROR rROR

25 0.07 0.03 0.15 0.06 0.0291 Age Income Deflator Saving Cumulative Savings rConsumption

In our initial plan (Spreadsheet 18.1), we envisioned consuming a level, nominal annuity

for the retirement years This is an inappropriate goal once we account for inflation, since it

would imply a declining standard of living starting at age 65 Its purchasing power at age 65

in terms of current dollars would be $64,542 (i.e., $181,362/2.81), and at age 90 only $30,792

(Check this!)

It is tempting to contemplate solving the problem of an inadequate retirement annuity by

increasing the assumed rate of return on investments However, this can only be accomplished

by putting your savings at risk Much of this text elaborates on how to do so efficiently; yet it

also emphasizes that while taking on risk will give you an expectation for a better retirement,

it implies as well a nonzero probability of doing a lot worse At the age of 30, you should be

able to tolerate some risk to the retirement annuity for the simple reason that if things go

wrong, you can change course, increase your savings rate, and work harder As you get older,

this option progressively fades, and increasing risk becomes less of a viable option If you do

choose to increase risk, you can set a “safety-first target” (i.e., a minimum acceptable goal) for

the retirement annuity and continuously monitor your risky portfolio If the portfolio does

poorly and approaches the safety-first target, you progressively shift into risk-free bonds—you

may recognize this strategy as a version of dynamic hedging

The difficulty with this strategy is twofold: First it requires monitoring, which is

time-consuming and may be nerve-racking as well Second, when decision time comes, it may be

psychologically hard to withdraw By shifting out of the risky portfolio if and when your

port-folio is hammered, you give up any hope of recovery This is hard to do and many investors

fail the test For these investors, therefore, the right approach is to stick with the safe, lower

ROR and make the effort to balance standard of living before and after retirement Avoiding

sleepless nights is ample reward

Therefore, the only variable we leave under your control in this spreadsheet is the rate of

saving To improve retirement life style relative to the preretirement years, without

jeopar-dizing its safety, you will have to lower consumption during the saving years—there is no

free lunch

2 If you project a rate of inflation of 4%, what nominal ROR on investments would

you need to maintain the same real retirement annuity as in Spreadsheet 18.2?

An Alternative Savings Plan

In Spreadsheet 18.2, we saved a constant fraction of income But since real income grows over

time (nominal income grows at 7% while inflation is only 3%), we might consider deferring

our savings toward future years when our real income is higher By applying a higher savings

rate to our future (higher) real income, we can afford to reduce the current savings rate In

Spreadsheet 18.3, we use a base savings rate of 10% (lower than the savings rate in the

previ-ous spreadsheet), but we increase the savings target by 3% per year Saving in each year

there-fore equals a fixed savings rate times annual income (column B), times 1.03t By saving a

larger fraction of income in later years, when real income is larger, you create a smoother

pro-file of real consumption

Spreadsheet 18.3 shows that with an initial savings rate of 10%, compared with the

un-changing 15% rate in the previous spreadsheet, you can achieve a retirement annuity of

$59,918, larger than the $49,668 annuity in the previous plan

Notice that real consumption in the early years is greater than with the previous plan What

you have done is to postpone saving until your income is much higher At first blush, this plan

is preferable: It allows for a more comfortable consumption of 90% of income at the outset, a

consistent increase in standard of living during your earning years, all without significantly

af-fecting the retirement annuity But this program has one serious downside: By postponing the

Concept

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bulk of your savings to a later age, you come to depend on your health, longevity, and, moreominously (and without possibility of insurance), on a successful future career Put differently,this plan achieves comfort by increasing risk, making this choice a matter of risk tolerance.

3 Suppose you like the plan of tilting savings toward later years, but worry about theincreased risk of postponing the bulk of your savings to later years Is there any-thing you can do to mitigate the risk?

18.3 ACCOUNTING FOR TAXES

To initiate a discussion of taxes, let’s assume that you are subject to a flat taxrate of 25% ontaxable income less one exemption of $15,000 This is similar to several proposals for a sim-plified U.S tax code that have been floated by one presidential candidate or another prior toelections—at least when you add state taxes to the proposed flat rate An important feature ofthis (and the existing) tax code is that the tax rate is levied on nominal income and applies aswell to investment income (This is the concept of double taxation—you pay taxes when youearn income and then you pay taxes again when your savings earn interest) Some relief fromthe effect of taxing nominal dollars both in this proposal and the current U.S code is provided

by raising the exemption, annually, by the rate of inflation To adapt our spreadsheet to thissimple tax code, we must add columns for taxes and after-tax income The tax-adjusted plan

is shown in Spreadsheet 18.4 It adapts the savings plan of Spreadsheet 18.2

The top panel of the sheet deals with the earning years Column D adjusts the exemption(D2) by the price level (column C) Column E applies the tax rate (cell E2) to taxable income(column B ⫺ column D) The savings rate (F2) is applied to after-tax income (column B ⫺column E), allowing us to calculate cumulative savings (column G) and real consumption(column H) The formula view shows the detailed construction

As you might have expected, real consumption is lower in the presence of taxes, as are ings and the retirement fund The retirement fund provides for a real, before-tax annuity ofonly $37,882, compared with $49,668 absent taxes in Spreadsheet 18.2

sav-The bottom panel of the sheet shows the further reduction in real consumption due totaxes paid during the retirement years While you do not pay taxes on the cumulative savings

in the retirement plan (you did that already as the savings accrued interest), you do pay taxes

on interest earned by the fund while you are drawing it down These taxes are quite cant and further deplete the fund and its net-of-tax earning power For this reason, your

A tax code that

taxes all income

consumption annuity is lower in the early years when your fund has not yet been depleted and

earns quite a bit

In the end, despite a handsome income that grows at a real rate of almost 4%, an aggressive

savings rate of 15%, a modest rate of inflation, and a modest tax, you will only be able to

achieve a modest (but at least low-risk) real retirement income This is a reality with which

most people must struggle Whether to sacrifice more of today’s standard of living through an

increased rate of saving, or take some risk in the form of saving a real annuity and/or invest in

a risky portfolio with a higher expected return, is a question of preference and risk tolerance

One often hears complaints about the double taxation resulting from taxing income earned

on savings from dollars on which taxes were already paid It is interesting to see what

effec-tive tax rate is imposed on your lifetime earnings by double taxation To do so, we use

Spread-sheet 18.4 to set up your lifetime earnings, exemptions, and taxes:

Income

Total exemptions during working years 949,139

Taxes

Thus, double taxation is equivalent to raising the effective tax rate on long-term savers from

the statutory rate of 25% to an effective rate of over 32%

4 Would a 1% increase in the exemption compensate you for a 1% increase in the

tax rate?

Saving with a simple tax code

1 2 3 4 5 9 19 29 39 40 41 42 43 47 52 57 62 67 68

18.4 THE ECONOMICS OF TAX SHELTERS

Tax sheltersrange from the simple to the mind-bogglingly complex, yet they all have onecommon objective: to postpone payment of tax liabilities for as long as possible We knowalready that this isn’t small fry Postponement implies a smaller present value of tax payment,and a tax paid with a long delay can have present value near zero However, delay is neces-sarily beneficial only when the tax rate doesn’t increase over time If the tax rate on retirementincome is higher than during earning years, the value of a tax deferral may be questionable; ifthe tax rate will decline, deferral is even more preferable

A Benchmark Tax Shelter

Postponing tax payments is the only attainable (legal) objective since, whenever you have able income, a tax liability is created that can (almost) never be erased.4For this reason, a

tax-benchmark tax shelter postpones all taxes on savings and the income on those savings In this

case, your entire savings account is liable to taxation and will be paid upon retirement, as youdraw down the retirement fund This sort of shelter is actually equivalent to the tax treatment

of Individual Retirement Accounts (IRAs) which we discuss later, so we will describe thisstructure as having an “IRA style.”

To examine the impact of an IRA-style structure (assuming you could shelter all your ings) in a situation comparable to the nonsheltered flat-tax case, we maintain the same con-sumption level as in Spreadsheet 18.4 (flat tax with no shelter), but now input the new,sheltered savings plan in Spreadsheet 18.5 This focuses the entire effect of the tax shelter ontoretirement consumption

sav-In this sheet, we input desired real consumption (column H, copied from Spreadsheet 18.4).Taxes (column E) are then calculated by applying the tax rate (E2) to nominal consumptionless the exemption (H ⫻ C ⫺ D) The retirement panel shows that you pay taxes on all with-drawals—all funds in the retirement account are subject to tax

The results are quite surprising The tax protection means faster accumulation of the tirement fund, which grows to $3.7 million (column G), compared with only $1.9 millionwithout the shelter, but you also owe taxes on the entire amount You pay taxes as you drawincome from the retirement funds, and this tax load results in an effective tax rate of about20% on your withdrawals (E68/B68) Still, your real retirement annuity ($60,789) is fargreater than the average $35,531 absent the shelter, a result of the earning power of the sav-ings on which you postponed taxes Note that the source of effectiveness of the shelter istwofold: postponing taxes on both savings and the investment earnings on those savings

re-5 With the IRA-style tax shelter, all your taxes are due during retirement Is the off between exemption and tax rate different from the circumstance where youhave no shelter?

trade-The Effect of the Progressive Nature of the Tax Code

Because of the exemption, the flat tax is somewhat progressive: taxes are an increasing tion of income as income rises For very high incomes, the marginal tax rate (25%) is onlyslightly higher than the average rate For example, with income of $50,000 at the outset, theaverage tax rate is 17.5% (.25 ⫻ 35,000/50,000), and grows steadily over time In general,with a flat tax, the ratio of the average to marginal rate equals the ratio of taxable to gross

income This ratio becomes 89 at age 45 (check this) at which point the average tax rate is

above 22% The current U.S tax code, with multiple income brackets, is much more

progres-sive than our assumed structure

In Spreadsheet 18.6 we work with a more progressive taxstructure that is closer to the

U.S Federal tax code augmented with an average state tax Our hypothetical tax schedule is

described in Table 18.1

Spreadsheet 18.6 is identical to Spreadsheet 18.4, the only difference being the tax built

into column E according to the schedule in Table 18.1

Despite the more progressive schedule of this tax code, at the income level we assume, you

would end up with a similar standard of living This is due to the large lower-rate bracket

Although the lifetime tax rate is higher, 34.66% compared with 32.13% for the flat tax, you

actually pay lower taxes until you reach the age of 41 The early increased savings offset some

of the bite of the overall higher tax rate Another important result of the nature of this code is

the lower marginal tax rate upon retirement when taxable income is lower This is the

envi-ronment in which a tax shelter is most effective, as we shall soon see

Spreadsheet 18.7 augments the progressive tax code with our benchmark (IRA-style) tax

shelter that allows you to pay taxes on consumption (minus an exemption) and accumulate tax

liability to be paid during your retirement years The construction of this spreadsheet is

iden-tical to Spreadsheet 18.5, with the only difference being the tax structure built into column E

We copied the real pre-retirement consumption stream from Spreadsheet 18.6 to focus the

=(G2-C2)/(1+C2)

rConsumption 35062.5

36223.7712378641 116364.980523664

as income rises.

effect of the tax shelter on the standard of living during the retirement years Spreadsheet 18.7shows that the lower tax bracket during the retirement years allows you to pay lower taxesover the life of the plan and significantly increases retirement consumption The use of theIRA-style tax shelter increases the retirement annuity by an average of $34,000 a year, a bet-ter improvement than we obtained from the shelter with the flat tax.

The effectiveness of the shelter also has a sort of hedge quality If you become fortunateand strike it rich, the tax shelter will be less effective, since your tax bracket will be higher atretirement However, mediocre or worse outcomes will result in low marginal rates upon re-tirement, making the shelter more effective and the tax bite lower

6 Are you indifferent between an increase in the low-income bracket tax rate versus

an equal increase in the high bracket tax rates?

18.5 A MENU OF TAX SHELTERS Individual Retirement Accounts

Individual Retirement Accounts (IRAs) were set up by Congress to increase the incentives tosave for retirement The limited scope of these accounts is an important feature Currently,annual contributions are limited to $3,000 with a scheduled increase to $4,000 in tax years2005–2007 and then to $5,000 afterward Workers 50 years of age and up can increase annual

Income tax schedule

used for the

*The capital gains tax rate is assumed to be 8% when income is in the low two brackets and 28% for the highest bracket.

**Current exemption with this code is assumed to be $10,000 The exemption and tax brackets are adjusted for future inflation.

contributions by another $1,000 IRAs are somewhat illiquid (as are most shelters), in that

there is a 10% penalty on withdrawals prior to age 591⁄2 However, allowances for early

with-drawal with no penalty for qualified reasons such as (one-time) purchase of a home or higher

education expenses substantially mitigate the problem

There are two types of IRAs to choose from; the better alternative is not easy to determine

Traditional IRA Contributions to traditional IRAaccounts are tax deductible, as are the

earnings until retirement In principle, if you were able to contribute all your savings to a

tra-ditional IRA, your savings plan would be identical to our benchmark tax shelter (Spreadsheets

18.5 and 18.7), with the effectiveness of tax mitigation depending on your marginal tax rate

upon retirement

Roth IRA ARoth IRAis a variation on the traditional IRA tax shelter, with both a

draw-back and an advantage Contributions to Roth IRAs are not tax deductible However, earnings

on the accumulating funds in the Roth account are tax-free, and unlike a traditional IRA, no

taxes are paid upon withdrawals of savings during retirement The trade-off is not easy to

eval-uate To gain insight and illustrate how to analyze the trade-off, we contrast Roth with

tradi-tional IRAs under our two alternative tax codes

Roth IRA with the Progressive Tax Code

As we have noted, a traditional IRA is identical to the benchmark tax shelter set up under

two alternative tax codes in Spreadsheets 18.5 and 18.7 We saw that, as a general rule, the

effectiveness of a tax shelter depends on the progressivity of the tax code: lower tax rates

dur-ing retirement favor the postponement of tax obligations until one’s retirement years

How-ever, with a Roth IRA, you pay no taxes at all on withdrawals during the retirement phase In

this case, therefore, the effectiveness of the shelter does not depend on the tax rates during the

retirement years The question for any investor is whether this advantage is sufficient to

com-pensate for the nondeductibility of contributions, which is the primary advantage of the

retirement.

Roth IRA

Contributions are not tax sheltered, but investment earnings are tax free.

To evaluate the trade-off, Spreadsheet 18.8 modifies Spreadsheet 18.7 (progressive tax) toconform to the features of a Roth IRA, that is, we eliminate deductibility of contributions andtaxes during the retirement phase We keep consumption during the earning years the same asthey were in the benchmark (traditional IRA) tax shelter to compare the standard of living inretirement afforded by a Roth IRA tax shelter

Table 18.2 demonstrates the difference between the two types of shelters The first lineshows the advantage of the traditional IRA in sheltering contributions Taxes paid during theworking years are lower, yet taxes during the retirement years are significant and, later in life,you pay less tax with Roth IRAs (line 2) For the middle-class income we examine here, this

is not sufficient to make Roth IRA more attractive, as the after-tax annuities demonstrate Thereason is that early tax payments weigh more heavily than later payments However, one canfind situations in which a Roth IRA will be more advantageous This is why it is important forinvestors to check their unique circumstances Those who are not able to do so themselves canlog on to one of the many websites that provide tools to do so (e.g., http://www.quicken.com).Notice in Table 18.2 that the lifetime tax rate for saving with traditional IRAs is 39.37%.This is a result of large accumulation of earnings on savings that are taxed on retirement andshows the importance of early accumulation Despite the higher lifetime taxes, this tax shelterends up with larger after-tax real consumption during retirement

Traditional IRA Roth IRA Taxes:

7 Suppose all taxpayers were like you, and the IRS wished to raise a fixed tax

reve-nue Would it be wise to offer the Roth IRA option?

401k and 403b Plans

These days the majority of employees receive retirement benefits in the form of a defined

con-tribution plan (see Chapter 17) These are named after the relevant sections of the U.S tax

code: 401k in the corporate sector and 403b in the public and tax-exempt sectors These are

quite similar and the discussion of 401k plans applies to 403b plans as well

401k planshave two distinct features First and foremost, your employer may match your

contribution to various degrees, up to a certain level This means that if you elect not to

par-ticipate in the plan, you forego part of your potential employment compensation Needless to

say, regardless of tax considerations, any employee should contribute to the plan at least as

much as the employer will match, except for extreme circumstances of cash needs While

some employees may face cash constraints and think they would be better off skipping

con-tributions, in many circumstances, they would be better off borrowing to bridge the liquidity

shortfall while continuing to contribute up to the level matched by the employer

The second feature of the plan is akin to a traditional IRA in tax treatment and similar in

other restrictions Contributions to 401k plans are restricted (details can be found on many

websites, e.g., http://www.Morningstar.com), but the limits on contributions generally exceed

the level matched by the employer Hence you must decide how much of your salary to

con-tribute beyond the level matched by your employer You can incorporate 401k plans, like the

traditional IRA, in your savings-plan spreadsheet, review the trade-off, and make an informed

decision on how much to save

Risky Investments and Capital Gains as Tax Shelters

So far we limited our discussion to safe investments that yield a sure 6% This number,

coupled with the inflation assumption (3%), determined the results of various savings rules

under the appropriate tax configuration You must recognize, however, that the 6% return and

3% inflation are not hard numbers and consider the implications of other possible scenarios

over the life of the savings plan The spreadsheets we developed make scenario analysis quite

easy Once you set up a spreadsheet with a contemplated savings plan, you simply vary the

inputs for ROR (the nominal rate of return) and inflation and record the implications for each

scenario The probabilities of possible deviations from the expected numbers and your risk

tolerance will dictate which savings plan provides you with sufficient security of obtaining

your goals This sensitivity analysis will be even more important when you consider risky

investments

The tax shelters we have described allow you to invest in a broad array of securities and

mutual funds and you can invest your nonsheltered savings in anything you please Which

portfolio to choose is a matter of risk versus return That said, taxes lend importance to the

otherwise largely irrelevant aspect of dividends versus capital gains

According to current U.S tax law, there are two applicable capital gains rates for most

in-vestments: 20% if your marginal tax rate is higher than 27.5%, and 8%5if you are in a lower

tax bracket More importantly, you pay the applicable rate only when you sell the security

Thus, investing in non-dividend-paying securities is an automatic partial tax shelter with no

restrictions on contributions or withdrawals Because this investment is not tax deductible, it

a set percentage.

5 The rate goes up to 10% if you hold the security for less than five years.

is similar to a Roth IRA, but somewhat inferior in that you do pay a tax on withdrawal, ever low Still, such investments can be more effective than traditional IRA and 401k plans, as

how-we discussed earlier Since annual contributions to all IRAs and 401k plans are quite limited,investment in a low- or no-dividend portfolio may be the efficient shelter for many investorswho wish to exceed the contribution limit Another advantage of such portfolios is that youcan sell those securities that have lost value to realize capital losses and thereby reduce your

tax bill in any given year This virtue of risky securities is called the tax-timing option

Man-aging a portfolio with efficient utilization of the tax-timing option requires expert attention,however, and may not be appropriate for many savers

The average dividend yield on the S&P 500 stocks is less than 2%, and other indexes(such as Nasdaq) bear an even lower yield This means that you can easily construct a well-diversified portfolio with a very low dividend yield Such a portfolio allows you to utilize thetax advantage of capital gains versus dividends Spreadsheet 18.9 adapts Spreadsheet 18.6(progressive tax with no shelter) to a no-dividend portfolio of stocks, maintaining the samepreretirement consumption stream and holding the ROR at 6% Real retirement consumption,averaging $47,756, is almost identical to that supported by a Roth IRA (Spreadsheet 18.7).6

Sheltered versus Unsheltered Savings

Suppose your desired level of savings is double the amount allowed in IRAs and 401k (or403b) plans At the same time you wish to invest equal amounts in stocks and bonds Whereshould you keep the stocks and where the bonds? You will be surprised to know how manyinvestors make the costly mistake of holding the stocks in a tax-protected account and thebonds in an unsheltered account This is a mistake because most of the return from bonds is

in the form of taxable interest payments, while stocks by their nature already provide sometax shelter

S P R E A D S H E E T 1 8 9

Saving with no-dividend stocks under a progressive tax

1 2 3 4 5 9 19 29 39 40 41 42 43 47 52 57 62 67 68

Total 1,752,425 1,163,478 Real Annuity 49,153

Age Nom Withdraw Deflator Cum cap gains Exemption Taxes Funds Left rConsumption

Recall that tax shelters enhance the retirement annuity with two elements: (1) tax deferral

on contributions and (2) tax deferral on income earned on savings The effectiveness of each

element depends on the tax rate on withdrawals Of the two types of tax shelters we analyzed,

traditional IRA and 401k (or 403b) plans contain both elements, while a Roth IRA provides

only the second, but with the advantage that the tax rate on withdrawals is zero Therefore, we

need to analyze the stock–bond shelter question separately for each type of retirement plan

Table 18.3 shows the hierarchy of this analysis when a Roth IRA is used The difference is

apparent by comparing the taxes in each column With stocks inside and bonds outside the

shelter you pay taxes early and at the ordinary income rate When you remove stocks from and

move bonds into the shelter you pay taxes later at the lower capital gains rate

When you use either a traditional IRA or 401k plan, contributions are tax deferred

re-gardless of whether you purchase stocks or bonds, so we need to compare only taxes on

income from savings and withdrawal Table 18.4 shows the trade-off for a traditional IRA or

401k plan

The advantage ends up being the same as with the Roth IRA By removing stocks from and

moving bonds into the shelter you gain the deferral on the bond interest during the savings

phase During the retirement phase you gain the difference between the ordinary income and

the capital gains rate on the gains from the stocks

8 Does the rationale of sheltering bonds rather than stocks apply to preferred stocks?

18.6 SOCIAL SECURITY

Social Security(SS) is a cross between a pension and insurance plan It is quite regressive in

the way it is financed, in that employees pay a proportional (currently 7.65%) tax on gross

wages, with no exemption but with an income cap (currently $89,400) Employers match

em-ployees’ contributions and pay SS directly.7

Stocks No taxes Taxed at capital gains rate

7 Absent the SS tax, it is reasonable to assume that the amount contributed by employers would be added to your

pre-tax income, hence your actual contribution is really 15.3% For this reason, self-employed individuals are required to

contribute 15.3% to SS.

Social Security

Federally mandated pension plan established to provide minimum retirement benefits to all workers.

On the other hand, SS is progressive in the way it allocates benefits; low-income als receive a relatively larger share of preretirement income upon retirement Of the SS tax of7.65%, 6.2% goes toward the retirement benefit and 1.45% toward retirement healthcareservices provided by Medicare Thus, combining your payments with your employer’s, thereal retirement annuity is financed by 2 ⫻ 6.2 ⫽ 12.4% of your income (up to the aforemen-tioned cap); we do not examine the Medicare component of SS in this chapter.

individu-SS payments are made throughout one’s entire working life; however, only 35 years ofcontributions count for the determination of benefits Benefits are in the form of a lifetime realannuity based on a retirement age of 65, although you can retire earlier (as of age 62) or later(up to age 70) and draw a smaller or larger annuity, respectively One reason SS is projected

to face fiscal difficulties in future years is the increased longevity of the population The rent plan to mitigate this problem is to gradually increase the retirement age

cur-Calculation of benefits for individuals retiring in a given year is done in four steps:

1 The series of your taxed annual earnings (using the cap) is compiled The status of thisseries is shown in your annual SS statement

2 An indexing factor series is compiled for all past years This series is used to account forthe time value of your lifetime contributions

3 The indexing factors are applied to your recorded earnings to arrive at the AverageIndexed Monthly Earnings (AIME)

4 Your AIME is used to determine the Primary Insurance Amount (PIA), which is yourmonthly retirement annuity

All this sounds more difficult than it really is, so let’s describe steps 2 through 4 in detail

The Indexing Factor Series

Suppose your first wage on which you paid the SS tax was earned 40 years ago To arrive

at today’s value of this wage, we must calculate its future value over the 40 years, that is,

FV⫽ wage ⫻ (1 ⫹ g)40 The SS administration refers to this as the indexed earnings for thatyear, and the FV factor, (1 ⫹ g)40, is the index for that year This calculation is made for eachyear, resulting in a series of indexed earnings which, when summed, is the value today of theentire stream of lifetime taxed earnings

A major issue is what rate, g, to use in producing the index for each year SS uses for each

year the growth in the average wage of the U.S working population in that year Arbitrarily,the index for the most recent two years is set to 1.0 (a growth rate of zero) and then increasedeach year, going backward, by the growth rate of wages in that year For example, in the year

2001 the index for 1967 (35 years earlier) was 6.16768 Thus the 1967 wage is assumed tohave been invested for 35 years at 5.34% (1.053435⫽ 6.16768) The actual average growthrate of wages in the U.S over the years 1967–2001 was 5.48%8; the index is slightly lower be-cause the growth rate in the two most recent years prior to retirement has been set to zero Wage growth was not constant over these years For example, it was as high as 10.07% in1980–1981, and as low as 0.86% in 1992–1993 At the same time, the (geometric) averageT-bill rate over the years 1967–2001 was 6.53% and the rate of inflation 4.92%, implying a

real interest rate of 1.53% For retirees of 2002, the average real growth rate applied to their

SS contributions is about 0.40% (depending on how much they contributed in each year), nificantly lower than the real interest rate over their working years, but closer to the longer-term (1926–2001) real rate of 0.72% (See Table 5.2)

sig-8 We use a wage growth rate of 7% in our exercises, assuming our readers are well educated and can expect a higher than average growth Special attention must be given to this input (and the others) if you advise other people.

The Average Indexed Monthly Income

The series of a retiree’s lifetime indexed contributions (there may be zeros in the series for

periods when the retiree was unemployed) is used to determine the base for the retirement

annuity The 35 highest indexed contributions are identified, summed, and then divided by

35⫻ 12 ⫽ 420 to achieve your Average Indexed Monthly Income (AIME) If you worked less

than 35 years, all your indexed earnings will be summed, but your AIME might be low since

you still divide the sum by 420 If you worked more than 35 years, your reward is that only

the 35 highest indexed wages will be used to compute the average

The Primary Insurance Amount

In this stage of the calculation of monthly SS benefits, low-income workers (with a low

AIME) are favored in order to increase income equality The exact formula may change from

one year to the next, but the example of four representative individuals who retired in 2002

demonstrates the principle The AIME of these individuals relative to the average in the

pop-ulation and their Primary Insurance Amount (PIA) are calculated in Table 18.5

Table 18.5 presents the value of SS to U.S employees who retired in 2002 The first part of

the table shows how SS calculates the real annuity to be paid to retirees.9The results differ for

the four representative individuals One measure of this differential is the income replacement

rate (i.e., retirement income as a percent of working income) provided to the four income

brackets in Table 18.5 Low-income retirees have a replacement rate of 60.45%, more than

1.5 times that of the high-wage employees (37.91%)

The net after-tax benefits may be reduced if the individual has other sources of income,

because a portion of the retirement annuity is subject to income tax Currently, retired

house-holds with combined taxable income over $32,000 pay taxes on a portion of the SS benefits

At income of $44,000, 50% of the SS annuity is subject to tax and the proportion reaches 85%

9 The annuity of special-circumstance low-income retirees is supplemented.

Calculation of the retirement annuity of representative retirees of 2002

Real retirement annuity ⫽ PIA ⫻ 12 8,755 14,423 18,858 21,295

*Income is above the maximum taxable and income replacement cannot be calculated.

**Internal Rate of Return.

at higher income You can find the current numbers and replicate the calculations in Table 18.5

by logging on to http://www.ssa.gov/OACT/ProgData/nominalEarn.html This website alsoallows you to project Social Security benefits at various levels of sophistication

When evaluating the attractiveness of SS as an investment for current retirees (the bottompart of Table 18.5), we must consider current longevityfigures For a male, current remaininglife expectancy at age 65 is an additional 15.6 years, and for a female 19.2 years Using thesefigures, the current PIA provides male retirees an internal rate of return on SS contributions inthe range of 7.44–4.72%, and female retirees 7.76–5.18%.10 These IRRs are obtained bytaking 12.4% (the combined SS tax) of the series of 35 annual earnings of the four employees

as cash outflows The series of annuity payments (16 years for males and 19 for females), suming inflation at 3%, is used to compute cash inflows

as-To examine SS performance another way, the last line in the table shows the longevity(number of payments) required to achieve an IRR of 6% Except for the highest incomebracket, all have life expectancy greater than this threshold Why are these numbers so attrac-tive, when SS is so often criticized for poor investment performance? The reason benefits are

so generous is that the PIA formula sets a high replacement rate relative to the SS tax rate, theproportion of income taxed Taking history as a guide, to achieve an IRR equal to the rate ofinflation plus the historical average rate on a safe investment such as T-bills (with a historicalreal rate of 0.7%), the formula would need to incorporate a lower replacement rate With afuture rate of inflation of 3%, this would imply a nominal IRR of 3.7% Is the ROR assumed

in our spreadsheets (6%) the right one to use, or is the expected IRR based on past real ratesthe correct one to use? In short, we simply don’t know But averaging across the population,

SS may well be a fair pension plan, taking into consideration its role in promoting equality ofincome

The solvency of SS is threatened by two factors: population longevity and a replacement growth of the U.S population Over the next 35 years, longevity is expected toincrease by almost two years, increasing steady-state expenditures by more than 10% To keep

below-a level populbelow-ation (ignoring immigrbelow-ation) requires below-an below-averbelow-age of 2.1 children per fembelow-ale, yetthe current average of 1.9 is expected to decline further.11The projected large deficit, begin-ning in 2016, requires reform of SS Increasing the retirement age to account for increasedlongevity does not constitute a reduction in the plan’s IRR and therefore seems a reasonablesolution to deficits arising from this factor Eliminating the deficit resulting from populationdecline is more difficult It is projected that doing so by increasing the SS tax may require anincrease in the combined SS tax of as much as 10% within your working years Such a simplesolution is considered politically unacceptable, so you must expect changes in benefits.The question of privatizing a portion of SS so that investors will be able to choose port-folios with risk levels according to their personal risk tolerance has become a hot public policyissue Clearly, the current format that provides a guaranteed real rate is tailored to individualswith low risk tolerance Although we advocate that at least a portion of SS be considered as asafety-first proposition (with a very low-risk profile), investors who are willing to monitor andrebalance risky portfolios cannot be faulted for investing in stocks The main point withrespect to this option is that the media and even some finance experts claim that a long-terminvestment in stocks is not all that risky We cannot disagree more We project that with

11 Fertility rates in Europe, Japan, and (until recently) in China are even lower, exacerbating the problems of their Social Security systems.

appropriate risk adjustment, future retirees will find it difficult to beat the SS plan and should

be made fully aware of this fact.12

9 Should you consider a dollar of future Social Security benefits as valuable as a

dollar of your projected retirement annuity? For example, suppose your target is a

real annuity of $100,000 and you project your SS annuity at $20,000 Should you

save to produce a real annuity of $80,000?

18.7 CHILDREN’S EDUCATION AND

L ARGE PURCHASES

Sending a child to a private college can cost a family in excess of $40,000 a year, in current

dollars, for four years Even a state college can cost in excess of $25,000 a year Many

fami-lies will send two or more children to college within a few years, creating a need to finance

large expenditures within a few years Other large expenditures such as a second home (we

deal with the primary residence in the next section) or an expensive vehicle present similar

problems on a smaller scale

The question is whether planned, large outflows during the working years require a major

innovation to our planning tools The answer is no All you need to do is add a column to your

spreadsheet for extra-consumption expenditures that come out of savings As long as

cumula-tive savings do not turn negacumula-tive as the outflows take place, the only effect to consider is the

reduction in the retirement annuity that results from these expenditures To respond to a

lower-than-desired retirement annuity you have four options: (1) increase the savings rate, (2) live

with a smaller retirement annuity, (3) do away with or reduce the magnitude of the

expendi-ture item, or (4) increase expected ROR by taking on more risk Recall though, that in Section

18.2, we suggested option 4 isn’t viable for many investors

The situation is a little more complicated when the extra-consumption expenditures create

negative savings in the retirement plan In principle, one can simply borrow to finance these

expenditures with debt (as is common for large purchases such as automobiles) Again, the

primary variable of interest is the retirement annuity The problem, however, is that if you

arrive at a negative savings level quite late in your savings plan, you will be betting the farm

on the success of the plan in later years Recalling, again, the discussion of Section 18.2, the

risk in later years, other things being equal, is more ominous since you will have little time to

recover from any setbacks

An illuminating example requires adding only one column to Spreadsheet 18.2, as shown

in Spreadsheet 18.10 Column G adds the extra-consumption expenditures We use as input

(cell G2) the current cost of one college year per child—$40,000 We assume your first child

will be collegebound when you are 48 years old and the second when you are 50 The

expen-ditures in column G are inflated by the price level in column C and subtracted from

cumula-tive savings in column E

The real retirement annuity prior to this extra-consumption expenditure was $48,262, but

“after-children” only $22,048, less than half The expenditure of $320,000 in today’s dollars

cost you total lifetime real consumption of 25 ⫻ ($48,262 ⫺ $21,424) ⫽ $6,710,950 because

12 Here, again, we collide with those who consider stocks low-risk investments in the long run (some of them esteemed

colleagues) One cannot overestimate the misleading nature of this assessment (see the Appendix to Chapter 6) The

difference between the 35-year average real rate over 1967–2001 (1.53%) and 1932–1966 ( ⫺1.05%), was 2.58%!

Over long horizons, such a difference has staggering effects on retirement income Check your spreadsheets to see the

impact of a 1% change in ROR.

Concept

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of the loss of interest on the funds that would have been saved If you change the input in G2

to $25,000 (reflecting the cost of a public college), the retirement annuity falls to $32,405, aloss of “only” 35% in the standard of living

10 What if anything should you do about the risk of rapid increase in college tuition?

18.8 HOME OWNERSHIP:

THE RENT-VERSUS-BUY DECISION

Most people dream of owning a home and for good reason In addition to the natural desire forroots that goes with owning your home, this investment is an important hedge for most fami-lies Dwelling is the largest long-term consumption item for most people and fluctuations inthe cost of dwelling are responsible for the largest consumption risk they face Dwelling costs,

in turn, are subject to general price inflation, as well as to significant fluctuations specific togeographic location This combination makes it difficult to hedge the risk with investments insecurities In addition, the law favors home ownership in a number of ways, chief of which istax deductibility of mortgage interest

Common (though not necessarily correct) belief is that the mortgage tax break is the majorreason for investing in rather than renting a home In competitive markets, though, rents willreflect the mortgage tax-deduction that applies to rental residence as well Moreover, homesare illiquid assets and transaction costs in buying/selling a house are high Therefore, pur-chasing a home that isn’t expected to be a long-term residence for the owner may well be aspeculative investment with inferior expected returns The right time for investing in yourhome is when you are ready to settle someplace for the long haul Speculative investments inreal estate ought to be made in a portfolio context through instruments such as Real EstateInvestment Trusts (REITs)

With all this in mind, it is evident that investment in a home enters the savings plan in twoways First, during the working years the cash down payment should be treated just like anyother large extra-consumption expenditure as discussed earlier Second, home ownershipaffects your retirement plan because if you own your home free and clear by the time youretire, you will need a smaller annuity to get by; moreover, the value of the house is part ofretirement wealth

11 Should you have any preference for fixed versus variable rate mortgages?

18.9 UNCERTAIN LONGEVITY

AND OTHER CONTINGENCIES

Perhaps the most daunting uncertainty in our life is the time it will end Most people consider

this uncertainty a blessing, yet, blessing or curse, this uncertainty has economic implications

Old age is hard enough without worrying about expenses Yet the amount of money you may

need is at least linear in longevity, if not exponential Not knowing how much you will need,

plus a healthy degree of risk aversion, would require us to save a lot more than necessary just

to insure against the fortune of longevity

One solution to this problem is to invest in a life annuity to supplement Social Security

benefits, your base life annuity When you own a life annuity(an annuity that pays you

in-come until you die), the provider takes on the risk of the time of death To survive, the

provider must be sure to earn a rate of return commensurate with the risk Except for wars and

natural disasters, however, an individual’s time of death is a unique, nonsystematic risk.13It

would appear, then, that the cost of a life annuity should be a simple calculation of interest

rates applied to life expectancy from mortality tables Unfortunately, adverse selection comes

in the way

Adverse selectionis the tendency for any proposed contract (deal) to attract the type of

party who would make the contract (deal) a losing proposition to the offering party A good

example of adverse selection arises in health care Suppose that Blue Cross offers health

cov-erage where you choose your doctor and Blue Cross pays 80% of the costs Suppose another

HMO covers 100% of the cost and charges only a nominal fee per treatment If HMOs were

to price the services on the basis of a survey of the average health care needs in the population

at large, they would be in for an unpleasant surprise People who need frequent and expensive

care would prefer the HMO over Blue Cross The adverse selection in this case is that

high-need individuals will choose the plan that provides more complete coverage The individuals

that the HMO most wants not to insure are most likely to sign up for coverage Hence, to stay

in business HMOs must expect their patients to have greater than average needs, and price the

policy on this basis

Providers of life annuities can expect a good dose of adverse selection as well, as people

with the longest life expectancies will be their most enthusiastic customers Therefore, it is

advantageous to acquire these annuities at a younger age, before individuals are likely to know

much about their personal life expectancies The SS trust does not face adverse selection

since virtually the entire population is forced into the purchase, allowing it to be a fair deal on

both sides

Unfortunately we also must consider untimely death or disability during the working years

These require an appropriate amount of life and disability insurance, particularly in the early

stage of the savings plan The appropriate coverage should be thought of in the context of a

retirement annuity Coverage should replace at least the most essential part of the retirement

annuity

Finally, there is the need to hedge labor income Since you cannot insure wages, the least

you can do is maintain a portfolio that is uncorrelated with your labor income As the Enron

case has taught us, too many are unaware of the perils of having their pension income tied to

their career, employment, and compensation Investing a significant fraction of your portfolio

in the industry you work in is akin to a “Texas hedge,” betting on the horse you own

Concept

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13 For this reason, life insurance policies include fine print excluding payment in case of events such as wars,

epidemics, and famine.

life annuity

An annuity that pays you income until you die.

adverse selection

The tendency for any proposed deal to attract the type of party who would make the deal a losing proposition

to the offering party.

12 Insurance companies offer life insurance on your children Is this a good idea?

heav-One sort of insurance the market cannot supply is wage insurance If we could obtain wageinsurance, a savings plan would be a lot easier to formulate Moral hazardis the reason forthis void in the marketplace Moral hazard is the phenomenon whereby a party to a contract(deal) has an incentive to change behavior in a way that makes the deal less attractive to theother party.14For example, a person who buys wage insurance would then have an incentive

to consume leisure at the expense of work effort Moral hazard is also why insuring items formore than their market or intrinsic value is prohibited If your warehouse were insured for lotsmore than its value, you might have less incentive to prevent fires, an obvious moral hazard

In contrast, marriage provides a form of co-insurance that extends also to the issue oflongevity A married couple has a greater probability that at least one will survive to an olderage, giving greater incentive to save for a longer life Put differently, saving for a longer lifehas a smaller probability of going to waste A study by Spivak and Kotlikoff (1981)15simu-lated reasonable individual preferences to show that a marriage contract increases the dollarvalue of lifetime savings by as much as 25% Old sages who have been preaching the virtue

of matrimony for millennia must have known more about economics than we give themcredit for

Bequest is another motive for saving There is something special about bequest that entiates it from other “expense” items When you save for members of the next generation(and beyond), you double the planning horizon, and by considering later generations as well,you can make it effectively infinite This has implications for the composition of the savingsportfolio For example, the conventional wisdom that as you grow older you should graduallyshift out of stocks and into bonds is not as true when bequest is an important factor in thesavings plan

differ-Having discussed marriage co-insurance and bequest, we cannot fail to mention thatdespite the virtues of saving for the longest term, many individuals overshoot the mark When

a person saves for old age and passes on before taking full advantage of the nest egg, the estate

is called an “involuntary, intergenerational transfer.” Data shows that such transfers are spread Kotlikoff and Summers (1981)16estimate that about 75% of wealth left behind is ac-tually involuntary transfer This suggests that people make too little use of the market for lifeannuities Hopefully you will not be one of them, both because you will live to a healthy oldage and because you’ll have a ball spending your never-expiring annuity

wide-13 If matrimony is such a good deal, but you haven’t yet found a soul mate, shouldyou rush to surf the Web for a potential spouse?

behavior in a way that

makes the contract

less attractive to

the other party.

14 Moral hazard and adverse selection can reinforce each other Restaurants that offer an all-you-can-eat meal attract big eaters (adverse selection) and induce “normal” eaters to overeat (moral hazard).

15Laurence J Kotlikoff and Avia Spivack, “The Family as an Incomplete Annuities Market,” Journal of Political Economy, 89, no 2 (April 1981), pp 372–91.

16 Laurence J Kotlikoff and Lawrence H Summers, “The Role of Intergenerational Transfers in Aggregate Capital

Ac-cumulation,” The Journal of Political Economy, 89, no 4 (August, 1981), pp 706–32.

Concept

• The major objective of a savings plan is to provide for adequate retirement income.

• Even moderate inflation will affect the purchasing power of the retirement annuity

Therefore, the plan must be cast in terms of real consumption and retirement income

• From a standpoint of smoothing consumption it is advantageous to save a fixed or rising

fraction of real income However, postponement of savings to later years increases the risk

of the retirement fund

• The IRA-style tax shelter, akin to a consumption tax, defers taxes on both contributions

and earnings on savings

• The progressive tax code sharpens the importance of taxes during the retirement years

High tax rates during retirement reduce the effectiveness of the tax shelter

• A Roth IRA tax shelter does not shield contributions but eliminates taxes during

retirement Savers who anticipate high retirement income (and taxes) must examine

whether this shelter is more beneficial than a traditional IRA account

• 401k plans are similar to traditional IRAs and allow matched contributions by employers

This benefit should not be foregone

• Capital gains can be postponed and later taxed at a lower rate Therefore, investment in

low-dividend stocks is a natural tax shelter Investments in interest-bearing securities

should be sheltered first

• Social Security benefits are an important component of retirement income

• Savings plans should be augmented for large expenditures such as children’s education

• Home ownership should be viewed as a hedge against rental cost

• Uncertain longevity and other contingencies should be handled via life annuities and

appropriate insurance coverage

SUMMARY

KEY TERMS

Social Security, 639tax shelters, 632traditional IRA, 635

PROBLEM SETS

1 With no taxes or inflation (Spreadsheet 18.1), what would be your retirement annuity if

you increase the savings rate by 1%?

2 With a 3% inflation (Spreadsheet 18.2), by how much would your retirement annuity

grow if you increase the savings rate by 1%? Is the benefit greater in the face of

inflation?

3 What savings rate from real income (Spreadsheet 18.3) will produce the same retirement

annuity as a 15% savings rate from nominal income?

4 Under the flat tax (Spreadsheet 18.4), will a 1% increase in ROR offset a 1% increase in

the tax rate?

5 With an IRA tax shelter (Spreadsheet 18.5), compare the effect on real consumption

during retirement of a 1% increase in the rate of inflation to a 1% increase in the tax rate

6 With a progressive tax (Spreadsheet 18.6), compare an increase of 1% in the lower tax

bracket to an increase of 1% in the highest tax bracket

7 Verify that the IRA tax shelter with a progressive tax (Spreadsheet 18.7) acts as a hedge

Compare the effect of a decline of 2% in the ROR to an increase of 2% in ROR

8 What is the trade-off between ROR and the rate of inflation with a Roth IRA under a

progressive tax (Spreadsheet 18.8)?

9 Suppose you could defer capital gains income tax to the last year of your retirement

(Spreadsheet 18.9) Would it be worthwhile given the progressivity of the tax code?

10 Project your Social Security benefits with the parameters of Section 18.6

11 Using Spreadsheet 18.10, assess the present value of a 1% increase in college tuition as

a fraction of the present value of labor income

12 Give another example of adverse selection

13 In addition to expected longevity, what traits might affect an individual’s demand for alife annuity?

14 Give another example of a moral hazard problem

W E B M A S T E R

Retirement Calculator

As was discussed in Chapters 17 and 18 one of the major factors that affects

invest-ment performance is asset allocation A retireinvest-ment calculator that allows you to

spec-ify different allocations and different levels of desired income to test the ability to meet

your retirement goals is available at http://www3.troweprice.com/retincome/RIC Use

the calculator to answer the following questions:

1 What level of retirement assets will you need to support a retirement income

level of $7,000 per month with 90% certainty? Assume that you will retire when you are 60, you expect to live for 30 years after you retire, and your portfolio allocation is 60% stock, 30% bonds, and 10% cash Work in increments of

$100,000 in retirement assets.

2 How much would you need to have in retirement assets to meet the same goal

with a 99% certainty?

3 If you return to the original 90% certainty level, how much would you need in

retirement assets to meet your original goal with a 40% stock, 40% bond, and 20% cash allocation?

SOLUTIONS TO 1 When ROR falls by 1% to 5%, the retirement annuity falls to from $192,244 to $149,855 (i.e., by

22.45%) To restore this annuity, the savings rate must rise by 4.24 percentage points to 19.24% With this savings rate, the entire loss of 1% in ROR falls on consumption during the earning years.

2 Intuition suggests you need to keep the real rate (2.91%) constant, that is, increase the nominal rate

to 7.03 (confirm this) However, this will not be sufficient because the nominal income growth of 7% has a lower real growth when inflation is higher Result: You must increase the real ROR to compensate for a lower growth in real income, ending with a nominal rate of 7.67%.

3 There are two components to the risk of relying on future labor income: disability/death and career failure/unemployment You can insure the first component, but not the second.

4 Holding before-tax income constant, your after-tax income will remain unchanged if your average tax rate, and hence total tax liability, is unchanged:

Total tax ⫽ (Income ⫺ Exemption) ⫻ Tax rate, or T ⫽ (I ⫺E) ⫻ t

A 1% increase in the tax rate will increase T by 01(I ⫺ E) A 1% increase in the exemption will decrease T by 01 ⫻ E ⫻ t Realistically, I ⫺ E will be greater than E ⫻ t and hence you will be

worse off with the increase in exemption and tax rate.

5 The qualitative result is the same However, with no shelter you are worse off early and hence lose also the earning power of the additional tax bills.

Concept

6 No, an increase in the low-bracket tax rate applies to your entire taxable income, while an increase

in the high-bracket tax rate applies only to a fraction of your taxable income.

7 No, in your hypothetical case, the Roth IRA tax shelter produces less taxes yet a smaller real

retirement annuity The reason is the timing of the taxes The timing issue does not affect the

stream of tax revenues to the IRS because at any point in time, taxpayers are distributed over all

ages In this case, the IRS can replace all Roth IRAs with traditional IRAs and lower the tax rates.

The IRS will collect similar revenue each year, and retirees will enjoy higher real retirement

annuities.

8 No, in terms of cash income, preferred stocks are more similar to bonds.

9 Your projected retirement fund is risky because of uncertainty about future labor income and

future real returns on savings The projected Social Security real annuity is risky because of

political uncertainty about future benefits It’s hard to judge which risk is greater.

10 You can invest in savings accounts that yield a floating rate tied to an index of college tuition.

11 A fixed-rate mortgage is the lower risk, higher expected cost option Homeowners with greater

risk tolerance might opt for a variable-rate mortgage which is expected to average a lower rate

over the life of the mortgage.

12 In the old days, children were more than a bundle of joy; they also provided a hedge for old-age

income Under such circumstance, insuring children would make economic sense These days,

children may well be a financial net expenditure, ruling out insurance on economic grounds Other

nonfinancial considerations are a matter of individual preference.

13 Rushing into marriage for economic reasons is a very risky proposition A bad marriage can be a

financial, as well as an emotional, calamity.

650

AFTER STUDYING THIS CHAPTERYOU SHOULD BE ABLE TO:

Understand the principles of behavioral finance

Identify reasons why technical analysis may be profitable

Use the Dow theory to identify situations that technicianswould characterize as buy or sell opportunities

Use indicators such as volume, put/call ratios, breadth,short interest, or confidence indexes to measure the

“technical conditions” of the market

BEHAVIORAL FINANCE AND TECHNICAL

Related Websites

http://www.decisionpoint.com

This site is directed toward technical analysis.

http://bigcharts.marketwatch.com

The above site gives you substantial capabilities to

chart stocks and compare them to trends and other

market variables.

http://www.firstcap.com

This site offers free information and also subscription

services It features many technical trading tools.

http://www.thegumpinvestor.com/stocks/ technical_analysis/default.asp

This site provides information on charting and other technical indicators.

http://finance.yahoo.com

This site has extensive charting capability along with information on many technical indicators.

rational behavior on the part of investors Components of this behavior, likemean-variance optimization, suggest investors must be able to solve compli-cated equations to construct optimal portfolios Obviously, this assumption is unreal-istic The standard response to this criticism is that a large number of investorsintuitively behave in a reasonable way which, on average, is similar to mean-varianceoptimization Yet observations cannot confirm that this is the case either The Arbi-trage Pricing Theory (APT) provides another line of defense for the idea that rationalbehavior will dominate capital asset price formation This theory proposes that it willtake few professionals deploying large investment funds to dominate price formation

in security markets The evidence of persistent anomalies in asset prices, as logued in Chapter 8, leaves us with a conundrum: Are these anomalies just samplingphenomena, are they driven by institutional trade friction, or are they a result of per-sistent, widespread behavior that is inconsistent with the assumption of economictheory? Behavioral finance is a growing specialization in pursuit of a coherent theorythat explains market anomalies We describe some of the major tenets of this emerg-ing theory at the top of the chapter

cata-Regardless of origin, as long as anomalies in asset pricing persist, technicalanalysis may be considered a defensible tool to exploit observed, inefficient prices Assuch, technical analysis is part of the study of active portfolio management Its test is

in its ability to generate abnormal profits in this pursuit Technical analysis focusesmore on past price movements of a company or an index than on the underlyingfundamental determinants of future profitability Technicians believe that past priceand volume data signal future price movements As we lay out the basics of technicalanalysis in the second part of this chapter, we point out the contradictions be-tween the assumptions on which these strategies are based and the notion of well-functioning capital markets with rational and informed investors

19.1 WHAT IS BEHAVIORAL FINANCE?

The premise of behavioral finance is that conventional financial theory ignores people, andthat people make a difference Supporters suggest one reason for this failure is that data onprices and returns are easy to come by but studying behavior is more difficult The objective

of behavioral finance is to consider all explanations in the search for understanding security

returns

The search for explanations of price series that stand in contradiction to conventional els is difficult As in any science, new theories come up short on occasion and often remaincontroversial for some time We point out such examples in the field of behavioral finance Yet

mod-a field of science should never be judged mod-a fmod-ailure mod-as long mod-as its remod-ason for being—explmod-ainingpuzzling data—is still valid Behavioral finance is an infant science, yet it is important foranyone interested in finance to be knowledgeable about its essential developments

19.2 INDIVIDUAL BEHAVIOR

One of the major tenets of rational behavior is selfishness This is to say that the individualattempts to maximize his or her own welfare, with little attention paid to others’ welfare Yeteven casual observations confirm that this is not the case The summary provided here drawsheavily on Thaler (1992, 1993)

Cooperation and Altruism

We begin our analysis of cooperation with the famous “prisoner’s dilemma.” Two felons arecaught and separated from each other If both refuse to confess, they can be convicted on onlyminor charges and will each receive a one-year sentence If both confess, each will receive asentence of five years If only one confesses and gives evidence against the other, he goes freeand the other receives a 10-year sentence Examination of the possible outcomes shows thatthe dominant strategy, that is, the best strategy, not knowing what the other felon will do, is toconfess Thus, the rational strategy leads to a worse outcome than cooperation would have.Another example of suboptimal results due to lack of cooperation is called the tragedy ofthe commons A community of fishermen lives off a fertile strip of (common) fishing grounds

A fisherman’s daily catch depends on investment in equipment The aggregate investment termines whether the fishing grounds will be depleted over time If each fisherman maximizesthe net present value (NPV) of investment, they will deplete the grounds in a hurry No fisher-man takes into account the fact that his take reduces the stock of fish available to other fisher-men As a result, the grounds are over-fished It is the common “ownership” of fishinggrounds that induces a prisoner’s dilemma The declining state of the world’s fishing grounds

de-is testimony to the force of thde-is dynamic

It turns out, however, that under a variety of conditions, individuals do cooperate and willdefy predictions of economic theory A manifestation of such behavior is shown in various

forms of the ultimatum game Here, individual A is given $100 to divide with another vidual B A makes an offer to B, say $10 B has a choice of taking the offer, in which case A takes home $90 and B, $10 If B refuses the offer, both players get nothing Conventional ra- tional behavior would induce B to accept any offer, since the alternative is zero Knowing this, A’s rational offer is very small But experiments clearly show that many deviate from this ra- tional dictum You can explain this either by A’s anticipation that B will be insulted and hence reject a small offer, or by an altruistic motive of A to induce a reasonably fair allocation The

indi-degree to which people deviate from rational behavior varies greatly and is materially affected

by circumstances But the fact remains that investor decision making is often perturbed byvarious motives extraneous to conventional rationality

Bidding and the Winner’s Curse

How much should you bid on an auctioned item whose value, you believe, is equally likely to

be anywhere in the range of $6 to $10? Should your bid depend on who else is bidding?

Intu-ition calls for bidding the expected value of $8, regardless of how many participate in the

auc-tion The logic of this solution, however, misses this important question: What is the value of

the item, conditional on your winning the bid? Assuming all participants bid their expected

values, this question is really: What is the expected value of the item given that you win the

auction, i.e., that the maximum of N independent bids is your bid of $8? Surely, this expected

value depends on the number of estimates The larger the number of estimates, the lower is the

expected value given that you win the auction with a bid of $8 Thus, if you hold your bid

at your expected value while the number of bidders grows, the probability that if you win,

you have overbid grows and so does your expected loss This is the winner’s curse: if you

win the auction, everyone else must think the asset is worth less than you do, so you likely

have overpaid

Armed with this insight, you must bid less than your estimate of the expected value; in

game-theory parlance you must “shave your bid.” The optimal bid depends on the distribution

of the true value, the number of bidders, and the degree of independence of their estimates

If everyone bids optimally, the winner can expect to pay a fair value and, more generally,

assets traded in auctions would fetch a fair price Can we assume this to be the case?

Eco-nomic theorists would answer in the affirmative Faced with the observation that most bidders

do not have the knowledge required to derive the optimal bid, they would argue that rules of

thumb derived from experience eventually lead traders to avoid the winner’s curse

Experiments appear to contradict this assertion, however Findings suggest that the

learn-ing curve of participants in auctions is flat Moreover, even managers in the construction

in-dustry, where bidding is the normal way of lending contracts, did not show savvy in avoiding

the winner’s curse This leaves open the question of whether assets priced in auctions fetch a

fair value

The Endowment Effect, the Status Quo Bias, and Loss Aversion

What is the value of an item, say a Harley Davidson, to an individual? Economic theory takes

this value to be unambiguous given the individual’s tastes and resources It turns out this isn’t

so When asked to bid on the item, an individual may bid $5,000 Once in possession of an

item, however, that same individual may not be willing to sell it for less than $6,000 This

am-biguous preference is called the endowment effect, whereby an individual’s preference for a

good increases by virtue of ownership This ambiguity is part of a broader phenomenon called

the status quo bias Individuals appear to prefer the status quo over a new position even if, a

priori, the new position would have been preferred to the current position

Researchers explain the endowment effect and the status quo bias by a type of preference

called loss aversion, shown in Figure 19.1 In any given position, potential losses are given

more weight than gains as conventional utility theory would predict But the slope and origin

of the preference function will abruptly change with a change in wealth, that is, preferences

continuously vary as fortunes change, leading to decisions that are inconsistent with predictions

from economic theory One result is that opportunity costs are not equal to out-of-pocket costs

That is, forgone opportunities are valued less than perceived losses and investors will not

up-date portfolios to account for changes in security values in the manner predicted from

mean-variance considerations

Observed inconsistent behavior also manifests itself in intertemporal choices, producing

ambiguity in the time value of money For example, it has been estimated that individuals

con-sistently assign excessive discount rates (from 25% to as high as 300%) to savings on energy

cost when they can invest in items such as insulation or energy-efficient appliances But, searchers also find that individuals implicitly assign too low, even negative, time value whenthey choose the timing of a lottery prize Studies of individual choices show significant in-consistency in assigning discount rates for consumption that changes with the timing and mag-nitude of future cash flows More generally, refuting the theory of life-cycle consumption, itappears that young and old people consume too little and middle-aged people consume toomuch relative to predictions of conventional theory Moreover, consumption appears to be toohighly correlated with income and too little correlated with various forms of wealth such ashome equity and pension accumulation.

re-Mental Accounts

The behaviorists’ explanation of various inconsistencies in consumption and investmentbehavior is based on a system of “mental accounts” in which individuals mentally segregateassets into independent accounts rather than viewing them as part of a unified portfolio Onesuch set of accounts is equity in assets, current income, and future income With this break-down, the marginal propensity to consume (MPC) out of wealth, that is, the amount consumedfrom an increase of $1 in wealth depends on the “account” where the extra dollar appears.MPC from current income is close to 1.0, MPC from future income is close to zero, and MPCfrom equity is in-between As discussed in the nearby box, this separation of mental accountsserves to impose discipline on consumption behavior despite impatience to consume—futureincome and equity in assets accounts are preserved while consumption binges are limited tocurrent income

The “disposition effect,” another outcome of mental accounts and loss aversion, refers

to the tendency to sell winners too early in order to increase cash accounts and to hang on tolosers for too long to avoid realizing losses The fact that the demand of “disposition in-vestors” for a stock depends too heavily on the price history of the stock means that pricesmay close in on fundamentals only over time, imparting momentum to price evolution Grin-blatt and Han (2001) show that disposition effects can lead to momentum in stock prices even

if fundamentals follow a random walk

The perfect is the enemy of the good.

I write a lot about rational investing But none of us

is completely rational We trade too much We chase

hot funds We take a flier on dubious stocks And, more

often than not, we end up hurting our performance.

But I am unwilling to dismiss this behavior as mere

foolishness Why not? Seemingly foolish behavior can

help us with our struggle.

Saving Ourselves

When saving for financial goals, we are supposed to

figure out how much each goal will cost, make a

rea-sonable estimate of what return we are likely to earn

and then diligently save the appropriate sum every

month.

Sound like the way you go about saving money? Me

neither Saving is a messy business, because of the

con-stant temptation to spend.

To compensate for our lack of self-control, we

of-ten fall back on mental games For instance, we might

have a chunk of cash sitting in a money-market fund

earning 1%, which we have earmarked for our

tod-dler’s college education But right now, we need a

new car.

Financially, it would make sense to “borrow” from

the college fund and then pay the money back But

in-stead, we take out a car loan, even though the loan will

likely cost us far more than we are earning on the

money-market fund.

Why do we go this route? Mentally, we have

ear-marked the money-market fund for the kid’s college

education, and we don’t trust ourselves to replenish the

account if we dip into it.

“Lots of us know that we won’t make those payments

to ourselves,” says John Nofsinger, author of

“Invest-ment Madness” and a finance professor at Washington

State University in Pullman, Wash “Mental accounting

helps us stay disciplined.”

Winning by Losing

The evidence is undeniable: Market-tracking index

funds outperform actively managed stock funds

De-spite this lackluster performance, actively managed

funds still account for 91% of all stock-fund assets.

Why do we continue to bank so heavily on a losing

proposition?

It seems we like having the chance, however slim, to

beat the market In fact, it makes us more inclined to

invest in stocks We also find it comforting when

professional stock pickers watch over our money Their

oversight gives us added confidence in our strategy and makes us more tenacious during rough markets.

To be sure, all this is likely to cost us, with the price paid in market-lagging performance But when we suf- fer this performance penalty, maybe we are getting our money’s worth.

Are we misguided? Maybe not “Even if the stocks don’t turn out to be better than other stocks, at least it gives us the courage to get started,” Prof Nofsinger notes.

Injecting Fun

While many investors struggle to find the courage to buy stocks, some folks have too much confidence These investment junkies buy and sell stocks like crazy, thereby incurring exorbitant trading costs and taking unnecessary risks.

Still, such enthusiasm isn’t all bad After all, if we are enthused about investing, we are probably more keenly aware of how much money we need for retire- ment and thus we are more likely to save enough.

The trick is to make sure our enthusiasm for trading doesn’t do too much damage.

“If you must trade and invest in foolish stocks, cate $10,000 or 5% of your money, whichever is smaller, to a fun-money account,” suggests Meir Stat- man, a finance professor at Santa Clara University in California “And then, very much like in Vegas, try to make the money last as long as possible.”

allo-Playing the Percentages

We should all decide what portion of our portfolio we want in stocks and then stick with this percentage through thick and thin But as many folks have discov- ered, this advice can be tough to follow.

Inevitably, some investors get skittish, and start ing in and out of the stock market This isn’t a smart strategy But it will probably lead to better results than simply leaving everything in a money-market fund.

danc-SOURCE: Jonathan Clements, “We All Make Irrational Decisions, But That May Not Be a Bad Thing.” Abridged from The Wall Street Journal online, March 26, 2002.

In sum, while economic theory relies on rational expectations and rational behavior, haviorists have documented evidence and explanations of fundamentals of behavior that areinconsistent with this theory However, the test of success of the efforts of the behaviorists

be-is in explaining deviations of assets prices from predictions of classic theory In the nextsection we provide an assessment of these efforts

19.3 ASSET RETURNS AND BEHAVIORAL

EXPL ANATIONS

It is natural for behaviorists to concentrate on documented anomalies in asset prices and tempt to explain them by behavior that is excluded by economic theory Here are the main-stream of these anomalies and offered explanations

at-Calendar Effects

Calendar effects are prominent among the anomalies documented in Chapter 8 on market ficiency An extraordinary pattern of abnormal returns occurs around the turn of the year andturn of months Behaviorists point to the following explanations:

ef-1 The timing of the flow of funds into the market is derived, at least in part, by the flow offunds to individual and institutional investors These tend to be concentrated aroundcalendar turns

2 “Window dressing” by institutional investors refers to trades timed to load quarterlybalance sheets with stocks of recently successful firms and rid them of stocks that haverecently stumbled

3 The publication of good and bad news under the control of the proprietors is mostlyissued around calendar turns

Cash Dividends

Dividend irrelevance in the absence of taxes and transaction costs is a fundamental tenet

of financial theory Tax-code discrimination against dividend income should, if anything,punish high-yield stocks Finally, the clientele effect predicts that, if investors exhibitedpreference for dividends over capital gains, supply of dividends by corporations wouldmaterialize so as to eliminate risk-adjusted differentials in expected returns Nevertheless,high dividends seem to endow stocks with a price premium

Preference for cash dividends can be justified by mental accounts, since dividends increasecurrent income at the expense of the “higher self control” equity account As evidence for suchbias in the population, Lease, Lewellen, and Schlarbaum (1976) compiled Table 19.1, whichshows that older and retired investors, those with the most funds to invest, value dividendsmore highly and concentrate their (better diversified!) portfolios in high income securities

Overraction and Mean Reversion

Perhaps the most notable influence of behavioral finance in explaining as set returns can befound in the literature of overreaction and mean reversion Investors assign a probability dis-tribution to future asset returns based on a relevant history of previous returns Appropriatereaction to an unexpected event (return) is to update one’s prior probability distribution byassigning a weight to the most recent event Overreaction results when investors assign too

large a weight on the most recent event Thus, if investors overreact, a negative event would

drive a stock price too low until additional developments lead investors to revalue the price in

line with fundamentals

In the presence of regular overreaction to changes in fundamentals, prices would tend to

reverse themselves as investors correct for the overreaction This tendency is called mean

reversion and can be detected by negative serial correlation in asset returns Numerous

stud-ies have uncovered negative correlation measured from weekly to five-year holding-period

returns Moreover, while anomalies such as calendar and dividend effects do not appear

strong enough to allow abnormal profits, the degree of serial correlation in stock returns is

such that profit opportunities appear plausible Using return histories, portfolios constructed

by buying losers and selling winners would have returned significant positive returns Thus,

overreaction suggested by mean reversion in stock returns appears to lend credibility to

be-havioral finance; using predictions from bebe-havioral analysis apparently can lead to profitable

portfolio strategies

19.4 CONTROVERSIAL EXPL ANATIONS FROM

BEHAVIORAL FINANCE

Empirical explanations from new fields of science often engender controversy and resistance

before they become conventional wisdom Behavioral explanations of asset returns are no

ex-ception, and we provide two examples

Closed-End Funds

The average closed-end fund sells at a discount of about 10% from its net asset value and

dis-counts of individual funds are quite volatile Such significant disdis-counts have long been

con-sidered a puzzle It is no wonder that closed-end fund discounts have attracted explanations

from behavioral finance

Stephen A Ross (2002) illustrates that observed discounts of closed-end fund values can

easily be explained by the funds’ expenses As a simple example, suppose a closed-end fund

invests its net asset value, NAV, in the market index (and hence adds no value from superior

management) The index has an expected return of r and pays out an annual dividend yield

Young Unmarried Males, Females, Professional Professionals Still at Mostly Retired Men & Managers Work Retired Males Investment Goal Rating:

Short term capital gains 2.19 2.00 1.86 1.50 1.53 Long-term capital gains 3.61 3.54 3.63 3.46 3.45

Percent of portfolio in

Average number of securities in portfolio 9.4 10.4 11.6 12.1 12.1

Source: R Lease, W Lewellen, and G Schlarbaum, “Market Segmentation: Evidence on the Individual Investor,” Financial Analysts Journal (1976), 53–60.

of Using the constant growth dividend discount model, the value of the fund is given by

P
 NAV/(r  g), where  NAV is the next dollar dividend and g is the growth rate of the fund’s assets The growth rate of the fund will be g
r   because the portfolio earns a rate r

and pays out  Thus, P
 NAV/(r  r  )
NAV as expected from a fund that provides

no added value Now suppose the fund charges the portfolio an annual fee at a rate of  In this

case, the growth rate of the fund’s portfolio is reduced to g
r (  ), and the value of the fund is reduced to: P
NAV /(r  r    )
NAV/(  ) Thus, the discount of price

from the net asset value of the portfolio will be (NAV P)/NAV
/(  ) With an annual

dividend yield of 2% and expense ratio of 5%, the discount will be 20% (.5/(2  5)
2)

By this calculation, observed discounts are not extraordinary

Obviously, closed-end funds are initiated and successfully sold when investors expect thefund management to do better than the market For example, if the portfolio’s expected return

is r  u and its risk is similar to that of the market index, then the required rate of return is r and the growth rate of assets will be g
r  u  (  ) If the expected abnormal return, u,

is greater than the expense ratio, , the fund will sell at a premium.1This explains why IPOs

(initial public offerings) of closed-end funds are at a premium; if investors do not expect u to

exceed, they won’t purchase the fund shares The fact that in most cases the premium turnsinto a discount indicates how difficult it is for management to fulfill these expectations in anearly efficient market

We can expect the abnormal expected return, u, to vary quite a bit as investors ingest the

volatile actual returns of the fund, and hence the discount itself will be volatile Also, it is not

surprising that u (hence the discount) is correlated across closed-end funds, as well as with

market returns and investor sentiment variables

An interesting question is why the same logic does not apply to open-end funds, since theycharge similar expense ratios The reason is that investors can always redeem open-end fundshares at the NAV Thus, the expense ratio is a period cost that accumulates to those who hold

on to their shares, but the stream of future expenses is not capitalized in the price of the fundshares Investors in closed-end funds do not have this option so the stream of future expensesmust be capitalized in the NAV, resulting in a discount from the portfolio value

When a discount of a closed-end fund becomes large, indicating that investors expect u to

be negative, the question arises: Why don’t investors purchase the fund and liquidate the folio at net asset value to instantly gain the discount? Investors can reasonably expect thatmanagement will not readily consent to the liquidation of the fund and hence such an eventwill not be likely (or inexpensive) Therefore, the possibility that the fund will be liquidatedmay not severely limit the size of potential discounts

port-Excessive Volatility of Stock Market Prices

Robert J Shiller (1981) rocked the world of economists and financial practitioners when heproduced evidence suggesting that the stock market is excessively volatile If true, this find-ing would be an outright refutation of the efficient market hypothesis (EMH) and must resultfrom irrational investment behavior Excessive volatility would be a natural outcome of over-reaction and lead to mean reversion It is consistent with predictions from behavioral finance

as explained earlier

To demonstrate that stock prices are excessively volatile Shiller used a long time series ofvalue and annual dividends on the S&P (the market) portfolio over the period 1871–1979,

1When u is too large, that is, g
r  u  (  )  r, then the dividend growth model is not valid In other words,

it is not plausible that u can be sustained in the long run In that case, we can recast the model as P
NAV/(  )

 M, where M is the present value of future abnormal returns, with the same results.

denoted by P1, P2, ,PT, and D1, D2, DT, respectively For each year, starting in 1871,

Shiller used a reasonable estimate of a discount factor to compute the present value of all

fu-ture dividends plus the present value of the terminal price and arrived at a rational price for the

market portfolio for that year This method of generating rational prices assumes that investor

expectations for future dividends and terminal price were in fact equal to the actual values

Having calculated rational stock prices, P t*, for all periods, Shiller compared the volatility of

the series of actual prices, P, to that of the rational prices, P* The standard deviation of actual

prices was more than five times that of rational prices Shiller argued that the excess volatility

of actual over rational prices could not be explained by data problems or by model

assump-tions, and several subsequent studies came to similar conclusions, even when allowing for a

time-varying discount rate

Shiller’s model assumes that volatility of dividends represents the volatility of stock

fun-damentals It is true that expected future dividends (knowing the appropriate discount rate) are

sufficient to compute a rational stock value, and it is plausible to take actual dividends to

rep-resent expected dividends It is not obvious, however, that the volatility of actual dividends

represents the volatility of stock fundamentals and, therefore, it is not obvious that the

vari-ance of the series of computed rational prices represents the varivari-ance we should expect from

actual prices

Consider an alternative model that derives the rational price from discounted future

earn-ings If it turned out that firms actually paid out a fixed proportion of earnings, then the

dis-counted earnings model would yield the same dividends as in Shiller’s model and identical

rational prices But in this case, the volatility of earnings will be the same as the volatility of

dividends and we would all agree that the volatility of the computed rational prices captures

the volatility of fundamentals

Of course, in reality firms do not pay out a fixed proportion of earnings, and thus the two

models will not yield the same results In fact, since earnings are far more volatile than

divi-dends, the volatility of rational prices will be much larger in the discounted earnings model

and will indicate that actual prices do not exhibit excess volatility While it may appear that

the discounted dividends model is the right one because it captures the actual payout ratios,

we should ask: Why then do firms vary payout ratios? The answer is that firms tend to smooth

dividends, and herein lies the problem with Shiller’s model The use of actual dividends to

compute rational prices and their volatility would be justified only if the dividend smoothing

were a response to transitory changes in earnings In that case, but only in that case, the

volatility of dividends would capture the volatility of fundamentals and the resultant volatility

of the computed rational prices would still be a valid benchmark for the volatility of actual

prices This, however, is the less likely situation Research suggests that managers do not

quickly adjust dividends to changes in fundamentals, particularly to worsening fundamentals

(explaining why reaction of stock prices to dividend cuts is so violent) Hence, the dividend

series is likely too smooth for tests of excessive volatility It appears, therefore, that

explana-tions from behavioral finance for “excess volatility” may have jumped the gun

As of now, then, behavioral theories successfully demonstrate that individual behavior is

not well approximated by standard utility analysis of economic theory But with the possible

exception of overreaction of stock prices, behavioral finance has yet to make its mark in

ex-plaining asset returns

19.5 TECHNICAL ANALYSIS

Technical analysis is in most instances an attempt to exploit recurring and predictable

pat-terns in stock prices to generate abnormal trading profits In the words of one of its leading

practitioners,

the technical approach to investment is essentially a reflection of the idea that the stock market moves in trends which are determined by the changing attitudes of investors to a variety of eco- nomic, monetary, political, and psychological forces The art of technical analysis, for it is an art,

is to identify changes in such trends at an early stage and to maintain an investment posture until

a reversal of that trend is indicated 2Technicians do not necessarily deny the value of fundamental information, such as we havediscussed in the three past chapters Many technical analysts believe stock prices eventually

“close in on” their fundamental values Technicians believe, nevertheless, that shifts in marketfundamentals can be discerned before the impact of those shifts is fully reflected in prices Asthe market adjusts to a new equilibrium, astute traders can exploit these price trends

Technicians also believe that market fundamentals can be perturbed by irrational or ioral factors More or less random fluctuations in price will accompany any underlying trend

behav-If these fluctuations dissipate slowly, they can be taken advantage of for abnormal profits.These presumptions, of course, clash head-on with those of the EMH and with the logic ofwell-functioning capital markets According to the EMH, a shift in market fundamentalsshould be reflected in prices immediately According to technicians, though, that shift will lead

to a gradual price change that can be recognized as a trend Such exploitable trends in stockmarket prices would be damning evidence against the EMH, as they would indicate profit op-portunities that market participants had left unexploited

A more subtle version of technical analysis holds that there are patterns in stock prices thatcan be explained, but that once investors identify and attempt to profit from these patterns,their trading activity affects prices, thereby altering price patterns This means the patterns thatcharacterize market prices will be constantly evolving, and only the best analysts who can

identify new patterns earliest will be rewarded We call this phenomenon self-destructing

pat-terns and explore it in some depth in the chapter

The notion of evolving patterns is consistent with almost but not-quite efficient markets Itallows for the possibility of temporarily unexploited profit opportunities, but it also viewsmarket participants as aggressively exploiting those opportunities once they are uncovered.The market is continually groping toward full efficiency, but it is never quite there

This is in some ways an appealing middle position in the ongoing debate between cians and proponents of the EMH Ultimately, however, it is an untestable hypothesis Tech-nicians will always be able to identify trading rules that would have worked in the past butneed not work any longer Is this evidence of a once viable trading rule that has now beeneliminated by competition? Perhaps But it is far more likely the trading rule could have beenidentified only after the fact

techni-Until technicians can offer rigorous evidence that their trading rules provide consistent

trading profits, we must doubt the viability of those rules As you saw in the chapter on the ficient market hypothesis, the evidence on the performance of professionally managed fundsgenerally does not support the efficacy of technical analysis

ef-19.6 CHARTING

Technical analysts are sometimes called chartists because they study records or charts of past

stock prices and trading volume, hoping to find patterns they can exploit to make a profit Inthis section, we examine several specific charting strategies

2Martin J Pring, Technical Analysis Explained, 2nd ed (New York: McGraw-Hill Book Company, 1985), p 2.

The Dow Theory

TheDow theory,named after its creator Charles Dow (who established The Wall Street

Jour-nal), is the grandfather of most technical analysis While most technicians today would view

the theory as dated, the approach of many more statistically sophisticated methods are

essen-tially variants of Dow’s approach The aim of the Dow theory is to identify long-term trends

in stock market prices The two indicators used are the Dow Jones Industrial Average (DJIA)

and the Dow Jones Transportation Average (DJTA) The DJIA is the key indicator of

underly-ing trends, while the DJTA usually serves as a check to confirm or reject that signal

The Dow theory posits three forces simultaneously affecting stock prices:

1 The primary trend is the long-term movement of prices, lasting from several months to

several years

2 Secondary or intermediate trends are caused by short-term deviations of prices from the

underlying trend line These deviations are eliminated via corrections when prices revert

back to trend values

3 Tertiary or minor trends are daily fluctuations of little importance.

Figure 19.2 represents these three components of stock price movements In this figure, the

primary trend is upward, but intermediate trends result in short-lived market declines lasting

a few weeks The intraday minor trends have no long-run impact on price

Figure 19.3 depicts the course of the DJIA during 1988 The primary trend is upward, as

ev-idenced by the fact that each market peak is higher than the previous peak (point F versus D

versus B) Similarly, each low is higher than the previous low (E versus C versus A) This

pat-tern of upward-moving “tops” and “bottoms” is one of the key ways to identify the underlying

primary trend Notice in Figure 19.3 that, despite the upward primary trend, intermediate trends

still can lead to short periods of declining prices (points B through C, or D through E)

The Dow theory incorporates notions of support and resistance levels in stock prices A

support levelis a value below which the market is relatively unlikely to fall Aresistance

levelis a level above which it is difficult to rise Support and resistance levels are determined

by the recent history of prices In Figure 19.3, the price at point D would be viewed as a

Dow theory

A technique that attempts to discern long- and short- term trends in stock market prices.

F I G U R E 19.2

Dow theory trends

Source: From Melanie F Bowman and Thom Hartle, “Dow Theory,” Technical Analysis of Stocks and Commodities, September 1990, p 690.

resistance level

A price level above which it is supposedly unlikely for a stock or stock index to rise.